Open Access

ARTICLE

Computational Solutions of a Delay-Driven Stochastic Model for Conjunctivitis Spread

Ali Raza^1,*, Asad Ullah², Eugénio M. Rocha¹, Dumitru Baleanu³, Hala H. Taha⁴, Emad Fadhal^5,*

1 Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, Aveiro, 3810-193, Portugal
2 Department of Physical Sciences, The University of Chenab, Gujrat, 50700, Pakistan
3 Department of Computer Science and Mathematics, Lebanese American University, Beirut, 1102 2801, Lebanon
4 Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia
5 Department of Mathematics and Statistics, College of Science, King Faisal University, Al Ahsa, 31982, Saudi Arabia

* Corresponding Authors: Ali Raza. Email: ; Emad Fadhal. Email:

(This article belongs to the Special Issue: Recent Developments on Computational Biology-II)

Computer Modeling in Engineering & Sciences 2025, 144(3), 3433-3461. https://doi.org/10.32604/cmes.2025.069655

Received 27 June 2025; Accepted 12 August 2025; Issue published 30 September 2025

Abstract

This study investigates the transmission dynamics of conjunctivitis using stochastic delay differential equations (SDDEs). A delayed stochastic model is formulated by dividing the population into five distinct compartments: susceptible, exposed, infected, environmental irritants, and recovered individuals. The model undergoes thorough analytical examination, addressing key dynamical properties including positivity, boundedness, existence, and uniqueness of solutions. Local and global stability around the equilibrium points is studied with respect to the basic reproduction number. The existence of a unique global positive solution for the stochastic delayed model is established. In addition, a stochastic nonstandard finite difference scheme is developed, which is shown to be dynamically consistent and convergent toward the equilibrium states. The scheme preserves the essential qualitative features of the model and demonstrates improved performance when compared to existing numerical methods. Finally, the impact of time delays and stochastic fluctuations on the susceptible and infected populations is analyzed.

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Keywords

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